A cross‐sector survey study was conducted between 2004 and 2005 among 121 software firms that adopted internet computing for the presence of strong order effects, which explain how, why and in which order radical innovations in information system (IS) are adopted. The following strong order effects were detected: (1) the amount of base innovations positively and directly influenced the amount of service innovation and the amount of process innovation, while the amount of service innovation partially mediates the impact of base innovation on process innovation; (2) the radicalness of base innovations directly and positively influences the radicalness of service innovation, while the impact of the radicalness of the base innovation on the radicalness of process innovations is fully mediated by the radicalness of service innovation; (3) the predominant sequence of initial adoption of radical information technology innovations is first in base innovations, followed by service innovations and finally by process innovations. Our study helps to better understand how and why radical innovations are adopted in ensembles by software firms. In consequence, software organizations should orchestrate flexible innovation strategies that recognize that radical innovations are interconnected and heterogeneous.